# Table 10: Random-Order Permutation Test

CA/GDP. 1000 random country orderings compared to income-ranked ordering.

If income ordering produces Z₁ values outside the 90% permutation envelope, the surface has income structure.

| Step | Income-ordered Z₁ | Perm median | Perm 90% range | Income %-ile | Outside 90%? |
|---:|---:|---:|:---|---:|:---|
| 20 | 46.31 | 9.14 | [-72.6, 94.4] | 76% |  |
| 40 | 36.84 | 8.37 | [-46.6, 64.0] | 80% |  |
| 60 | 41.65 | 8.31 | [-33.6, 49.3] | 91% |  |
| 80 | 33.97 | 6.80 | [-24.5, 40.7] | 90% |  |
| 100 | 37.78 | 7.38 | [-18.4, 32.4] | 98% | YES |
| 120 | 5.44 | 6.44 | [-13.2, 24.8] | 46% |  |
| 140 | 12.82 | 5.64 | [-9.1, 17.9] | 84% |  |
| 160 | 4.23 | 4.76 | [1.8, 8.7] | 31% |  |
| 162 | nan | 4.81 | [4.8, 4.8] | nan% |  |